Even if an ancient empire established the Common tongue, I couldn't see it surviving recognizably in the Points of Light. Every burg and city-state would develop its own linguistic conventions and variations on the old tongue, eventually, especially with the various different races (of different sizes and origins and such) being around and occasionally entering the communities or something. Heck, that's even before considering what effect the various tieflings, dragonborn, and such might have on speech patterns.
It'd be like me taking a trip to Scotland, visiting a very traditional fellow's home (as opposed to entering a big city where they might have lots of tourists or other exposure to foreigners speaking American English or British English), then trying to have a conversation on various topics. I'd barely follow anything they're saying, and they'd probably have trouble understanding many of my own words, pronunciation, and the occasional bit of American slang that I might use without realizing it. We'd know we're both speaking English, but very different, mostly incoherant English.
Without a more traditional D&D setting, I can't see there being enough trade and other interaction, or even just a few widespread guilds/organizations, that would maintain a reasonably-widespread understanding of the same Common tongue, with only minor local differences in dialect.